{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 抽样分布\n",
    "\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import chi2\n",
    "from scipy.stats import t\n",
    "from scipy.stats import f\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (6.0, 6.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pearson的$\\chi^2$-分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array(5.), array(10.), array(1.26491106), array(2.4))\n",
      "(array(15.), array(30.), array(0.73029674), array(0.8))\n",
      "(array(35.), array(70.), array(0.47809144), array(0.34285714))\n"
     ]
    }
   ],
   "source": [
    "chi2_froz_1 = chi2(5)\n",
    "chi2_froz_2 = chi2(15)\n",
    "chi2_froz_3 = chi2(35)\n",
    "\n",
    "xs_nd = np.linspace(3, 50, num=200)\n",
    "\n",
    "chi2_ys_nd_1 = chi2_froz_1.pdf(xs_nd)\n",
    "chi2_ys_nd_2 = chi2_froz_2.pdf(xs_nd)\n",
    "chi2_ys_nd_3 = chi2_froz_3.pdf(xs_nd)\n",
    "\n",
    "print(chi2_froz_1.stats(moments=\"mvsk\"))\n",
    "print(chi2_froz_2.stats(moments=\"mvsk\"))\n",
    "print(chi2_froz_3.stats(moments=\"mvsk\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f084f9f8588>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xs_nd, chi2_ys_nd_1, color='r', lw=2, label='df = 5')\n",
    "plt.plot(xs_nd, chi2_ys_nd_2, color='g', lw=2, label='df = 15')\n",
    "plt.plot(xs_nd, chi2_ys_nd_3, color='b', lw=2, label='df = 35')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gosset的t-分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array(0.), array(inf), array(nan), array(nan))\n",
      "(array(0.), array(3.), array(nan), array(nan))\n",
      "(array(0.), array(1.14285714), array(0.), array(0.5))\n"
     ]
    }
   ],
   "source": [
    "t_froz_1 = t(1)\n",
    "t_froz_2 = t(3)\n",
    "t_froz_3 = t(16)\n",
    "\n",
    "xs_nd = np.linspace(-4, 4, num=20)\n",
    "norm_ys_nd = norm.pdf(xs_nd)\n",
    "\n",
    "t_ys_nd_1 = t_froz_1.pdf(xs_nd)\n",
    "t_ys_nd_2 = t_froz_2.pdf(xs_nd)\n",
    "t_ys_nd_3 = t_froz_3.pdf(xs_nd)\n",
    "\n",
    "print(t_froz_1.stats(moments=\"mvsk\"))\n",
    "print(t_froz_2.stats(moments=\"mvsk\"))\n",
    "print(t_froz_3.stats(moments=\"mvsk\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f084f981be0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xs_nd, t_ys_nd_1, color='r', lw=2, label='df = 1')\n",
    "plt.plot(xs_nd, t_ys_nd_2, color='g', lw=2, label='df = 3')\n",
    "plt.plot(xs_nd, t_ys_nd_3, color='b', lw=2, label='df = 10')\n",
    "\n",
    "# 自由度越大, 月接近正态分布\n",
    "plt.plot(xs_nd, norm_ys_nd, color='black', lw=2, label='norm')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fisher的$\\mathcal{F}$-分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array(inf), array(inf), array(nan), array(nan))\n",
      "(array(1.2), array(0.6), array(2.75412149), array(20.06666667))\n",
      "(array(1.02040816), array(0.04295085), array(0.62436195), array(0.72788832))\n"
     ]
    }
   ],
   "source": [
    "f_froz_1 = f(1, 1)\n",
    "f_froz_2 = f(15, 12)\n",
    "f_froz_3 = f(100, 100)\n",
    "\n",
    "xs_nd = np.linspace(f_froz_3.ppf(0.01), f_froz_3.ppf(0.99), 100)\n",
    "\n",
    "f_ys_nd_1 = f_froz_1.pdf(xs_nd)\n",
    "f_ys_nd_2 = f_froz_2.pdf(xs_nd)\n",
    "f_ys_nd_3 = f_froz_3.pdf(xs_nd)\n",
    "\n",
    "print(f_froz_1.stats(moments=\"mvsk\"))\n",
    "print(f_froz_2.stats(moments=\"mvsk\"))\n",
    "print(f_froz_3.stats(moments=\"mvsk\"))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f084f8dfa20>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SBYDHHnuMF198kZUrVxIWFsbzaWVk81oNMzo6Osv3DQsLIzo6Ott9vby8eOWVVyhXrlyW7Vu2bOG+++7j/fffZ/369Wzbto1t27bRtWtXIiMjGT58OH5+fkRGRub7O9+JVNkUJCZm3AR1h7bwMmXgX/8yUyu+/rqZW9eK+v/OyJmrbO7atYsXX3yRDz74IMs9hbFjxzJ06FDmzJlDaGhovj7z/PnzlClThsDAwCzbv/766/TS0tOnT8/yWl6qYZYrV84uTV7Dhw/nT3/6E3379uWf//wnYAajXbhwga+//pqnHVBCVq70BQsXmpu4LVqAnSZHstyTT0KdOhARYSZ9EYazVtmsX78+qampzJ49m2rVqrFu3Tpat25Nq1at6NOnD8888wzLli2jY8eO6e9ZvHgxCxYsuOPnBgYGcuHCBVJSUti2bRvnzp274/55rYaZnyv9nLRq1YrRo0czaNCg9PsZwcHBFCtWjK+//prixYtz8OBBGtq7G11eqrIV5UOqbBat1FStQ0JMw8DUqVZHY18zZ5rvVauW1omJVkdjSJXNnD937ty5unXr1rpDhw76yy+/1FprfeXKFX3//ffr0NBQ3bdvX33+/Pn0z3n77bd1kyZNcj3eu+++q1u1aqVHjx6tg4OD07evXbs2y/fX2v7VMG369OmjGzRooMuXL69btWql4+Pj9alTp3S3bt10aGioHjZsmI6Li9Naa/3BBx/otm3b6vbt2+slS5Zk+3lSZVMU2K+/mlG35cqZgVl2mCbUaaSkmCqcBw+am9TPPmt1RFJl054WLlzI999/zzfffGN1KEVOqmyKAvv4Y7McM8a9Ej6AtzfYOnu8847pjircw9y5c/nxxx+ZOHGi1aG4HEn6HuzMGdOe7+0NzzxjdTSO8eCDcPfdZhJ1281q4fpGjBjBrFmzCAoKsjoUlyNJ34N9/jkkJ8PAgVCzptXROIaXV0YNof/8xzmu9p2tSVW4lsL+/UjS91DJyRkTkIwda20sjta7N7RqBRcuZHxnq/j5+XH58mVJ/KJAtNZcvnwZPz+/An+G3Mj1UEuWmHILDRuaG53OXjO/sBYvNr9oqlWDo0dNqQYrJCUlERUVRUJCgjUBCJfn5+dH9erV8fHxybI9rzdyZciKh7Jd8T7+uPsnfDAnuGbNYN8+mDHD3Li2go+Pz21D/4UoStK844HOnoVly8wo1UcftTqaouHllVFT6L33TPloITyRJH0PNGOG6cPerx94UueHwYOhQQM4ccJU4RTCE0nS9zBaw7RpZv2JJ6yNpah5e2fME/Dee5Caam08Qlgh16SvlPJTSj2vlDqhlBp9h/0GKaXWpT02KaUi07a/qZQ6lLZdpq222IYNcOSIuaF5771WR1P0RoyAGjXg0CHTxCWEp8nLlX4QcAOYc6edtNbfaq3DtNZhwAxgVqaX3097bUCBIxV2YbuB+9hj5srX0/j4mDr7YPrtC+Fpck36WuuTWuupQJ5ufSml/ICxgG189BVgrFJqo1LqhRzeM0YpFa6UCr948WIeQxf5FReXUV/+scesjcVKTzwBZcvCpk2wZYvV0QhRtBzRpv8cME9rfRVAaz0xre9oT2CkUuq2OqFa6yla6xCtdUjFihUdEJIA01c9Ph46djRlhz1VqVIZxdf++19rYxGiqBU46ae14S+8ZVtp4Angk2zekpK2vFbQY4rCsdWVf/hha+NwBs8/bwZo/fCDqbkvhKfIy43c6kqpcGAMMF4pNTPtpcrArTViXwG+0lrHZXr/35RSa4GfgAla6zP2CV3kx/nzsGqV6Zs/ZIjV0VgvKAhGjTK9mSZMsDoaIYqOlGHwEP/7n5kwvH9/c3Ur4PBhaNQIiheHU6egUiWrIxKi4KSevshiTlrfK2naydCgAdx/v5kj+PPPrY5GiKIhSd8DRETAtm0QEGBG4YoML79slp9+apK/EO5Okr4HsF3lP/SQ+82OVVhhYdCypbnnMW+e1dEI4XiS9N2c1jB3rlkfOdLaWJyRUuZeB8BHH5n/XkK4M0n6bm7nTlM/PijIXNWK2w0fbm7i7t4N69dbHY0QjiVJ380tTBtJ8eCDnll2IS98fTMGa330kbWxCOFokvTdmNYZSV/65t/ZM8+YrptLlsCxY1ZHI4TjSNJ3Y7t2ZTTtdO5sdTTOrVIlGDbMnCg//dTqaIRwHEn6bmzBArOUpp28ef55s5w2Da5ftzYWIRxFkr6byty0M3iwtbG4ipAQaNsWrlzJ6PEkhLuRpO+mbE07lSpBly5WR+M6bFf7n3wi3TeFe5Kk76ak107BDB5s7oHs3WtmGRPC3UjSd0PStFNwxYvDmDFmfdIka2MRwhEk6buh/fvNPLgVKkjTTkE8/bQpQb1oEZw+bXU0QtiXJH03tHixWfbvb5KXyJ+qVWHgQEhJgS+/tDoaIexLkr4bsiX9Bx6wNg5XZhuhO2UKJOVpdmghXIMkfTfzxx+wfTv4+0OPHlZH47pCQ6FxYzh7Fn780epohLAfSfpuxjYr1n33SRnlwlDKlGYAGaEr3IskfTcjTTv28+ij5hfTmjVw6JDV0QhhH5L03UhMDKxbZ/rl9+1rdTSur0yZjOklZTpF4S4k6buRpUtNj5PQUChXzupo3IOtiWf6dIiPtzQUIexCkr4bsTXtDBxobRzu5O67TT2e2FiYP9/qaIQoPEn6biIhAVauNOsDBlgbi7t5+mmz/OILa+MQwh4k6buJtWtN80NwMNSoYXU07mXIENO+/9tvppCdEK5Mkr6bWLrULPv1szYOd+Tvb3rygFztC9cnSd8NaJ2R9O+/39pY3NVTT5nl7Nlw7Zq1sQhRGJL03cC+fXDqlCkJHBJidTTuqWlT6NQJ4uLgm2+sjkaIgpOk7wZsV/l9+4KX/Is6jO1qX5p4hCuTFOEGpGmnaAwaZMY/7NgB4eFWRyNEwUjSd3EXL8LWrWbyDymw5lh+fhk3dKXksnBVkvRd3IoV5kZuWBgEBFgdjft78kmznDvXtO8L4WpyTfpKKT+l1PNKqRNKqdG57JuglFqX9hiYtq2NUmqDUmqzUmqCneIWaaRpp2g1aZJxQ3fePKujESL/8nKlHwTcAObkYd9zWuuwtMeitG1TgJFa645AsFKqQwFjFbdISoKffjLrUmCt6Niu9qdMsTYOIQoi16SvtT6ptZ4K5GX+oOS0q/rvlVJ1lFJl094Xp5SaBpQCWt/6JqXUGKVUuFIq/OLFi/n9Dh5r82a4etVM9lGnjtXReI7BgyEwELZtkxG6wvXYtU1fa11Pa90FmA28m7a5atrzj8nh14LWeorWOkRrHVKxYkV7huTWVqwwyz59rI3D05QoASNHmnW5oStcTYGTvlJqkFJqYU4vAzFa6xggDngC2AP0AbYU9JgiK1vS793b2jg80ZgxZjl7Nly/bm0sQuRHXm7kVldKhQNjgPFKqZlpL1UGGmfar5JSaqNSajXwEPB62kvPAIuAjcBWrfU2e34BTxUVBXv3QsmS5saiKFrNm5uSy1evwrffWh2NEHlXLLcdtNZRwG2D+7XWk4BJmZ5fADpns98aoG3hwhS3spVR7t4dfH2tjcVTPfmkqbz55ZcwapTV0QiRN9JP30UtX26W0rRjnaFDoVQpc0P94EGroxEibyTpu6CbN2H1arMuSd86pUrB8OFmfepUa2MRIq8k6bugLVtMed/GjeGuu6yOxrPZ+uzPnAmJidbGIkReSNJ3QdJrx3mEhECLFnDpEvzwg9XRCJE7SfouSJK+81Aq42pfmniEK5Ck72JOn87oqtn5tr5SwgoPP2wqcK5aBcePWx2NEHcmSd/F/PyzWXbtKl01nUXZsqbWPsDXX1sbixC5kaTvYmwF1u6919o4RFZPPGGWX30FKSnWxiLEnUjSdyEpKaYJASTpO5suXaBePdP8ZjsxC+GMJOm7kB07IDoaatUyCUY4D6Xg8cfNutzQFc5Mkr4Lydy0o5S1sYjbjRoF3t6wZAmcP291NEJkT5K+C7HdxO3Vy9o4RPaqVDEzmCUnm8FaQjgjSfou4upVMwG6t7cpsiacU+YmHq2tjUWI7EjSdxFr15oryHbtoEwZq6MROend21zxHz4MmzZZHY0Qt5Ok7yJs7fnStOPcihWDxx4z69OmWRuLENmRpO8ibO350lXT+f3pT2a5YAHExlobixC3kqTvAo4eNY+yZU2BL+Hc6tY1I6Zv3IB586yORoisJOm7ANtVfvfu5kaucH62EbrSZ184G0n6LsA2YUrPntbGIfJu4EAIDITwcNi92+pohMggSd/JpaTAmjVmXZK+6yhRAkaONOtyQ1c4E0n6Ti48HK5cMe3EtWtbHY3ID1uf/dmzISHB2liEsJGk7+RsBdbkKt/1BAdDq1YQEwPff291NEIYkvSdnCR912a72pcmHuEsJOk7sbg4U3rBywu6dbM6GlEQw4eb9v01a0y3WyGsJknfia1fD0lJ0Lq16QkiXE9gIAwebNa/+sraWIQASfpOTZp23IOtz/706aZ+khBWkqTvxGxJv0cPa+MQhdOpEzRoAGfOwMqVVkcjPJ0kfSd1+jQcOAAlS0L79lZHIwpDZtUSzkSSvpP65RezDA2F4sWtjUUU3qOPmgqcS5fC2bNWRyM8mSR9JyWlF9xL5crQr58ZYT1jhtXRCE8mSd8JaZ1xpS+zZLmPzH32ZVYtYZVck75Syk8p9bxS6oRSavQd9vNXSs1WSq1VSv2mlGqYtv1NpdQhpdQ6pdQPdozdbR06ZG76VaoEzZpZHY2wl/vug2rV4MgR0x1XCCvk5Uo/CLgBzLnTTlrreGC81rorMA14NtPL72utw7TWAwocqQexNe306GFuAgr34O2dMcHKl19aG4vwXLkmfa31Sa31VCApD/vaxhxWBY6lrV8BxiqlNiqlXsjufUqpMUqpcKVU+MWLF/MYuvuyJX1p2nE/f/qTOZF/9x1ER1sdjfBEdm/TV0o9ANwNTAbQWk/UWocAPYGRtmafzLTWU7TWIVrrkIoVK9o7JJeSnAzr1pl16Z/vfmrVMjfnExNhzh1/OwvhGAVO+kqpQUqphbdsexwYDAzWWt869jAlbXmtoMf0BOHhcPUq1K8PNWtaHY1wBNsI3S+/lBu6ougVy20HpVR1YDGmySZRKdVNa/0oUBlonGm/EGAKsBn4WSl1U2vdSyn1N6AXoIEJWuszDvgebiNze75wT/37Q4UKsHcvbNsGbdpYHZHwJLkmfa11FHDbdNxa60nApEzPw4HbZnDVWr8HvFe4MD2HdNV0f76+ZrDWhx+aq31J+qIoST99J3L9OmzZYm70de1qdTTCkZ580iy/+QauSYOnKEKS9J3Ipk1w86aZbalcOaujEY7UqJEpxHb9OsybZ3U0wpNI0nci0rTjWcaMMUvpsy+KkiR9JyJJ37MMGmQmWdm2DXbtsjoa4Skk6TuJ6GjYudNU1OzY0epoRFEoUQJGjjTrcrUviookfSexdq3ps92hA/j7Wx2NKCq2Jp45cyA+3tpYhGeQpO8kpGnHMzVvDm3bQmwsLFyY+/5CFJYkfSch9XY8l6375pQp1sYhPIMkfSfwxx8QGQkBAdC6tdXRiKI2bJj5t9+yBfbtszoa4e4k6TsBW9NOWJiZUk94lpIlM27oytW+cDRJ+k5A2vOF7YburFlyQ1c4liR9i8nUiAIgONjU4LlyRW7oCseSpG+xQ4fg7FkICoKmTa2ORljJdrX/xRfWxiHcmyR9i9mu8rt1k6kRPZ3thu7WrabsshCOIEnfYtK0I2zkhq4oCpL0LZSSkjE1oiR9AfDUU2Y5a5apwCmEvUnSt9COHebGXZ06Zu5UIVq2hHbtzAjd+fOtjka4I0n6FpKmHZGdp582y88/tzYO4Z4k6VtozRqzlKQvMhsyBMqWNSWXt2+3OhrhbiTpWyQx0cyUBTI1osiqRAkYPdqsS/dNYW+S9C2ydSvcuGGqLFaqZHU0wtnYbujOnWva94WwF0n6FpH2fHEnDRuaX4DXr5ta+0LYiyR9i0jSF7mx3dD97DNTrkMIe5Ckb4GrV+H338HbG7p0sToa4aweeAAqVzbllm33f4QoLEn6FtiwwQzMatMGSpe2OhrhrIoXhyeeMOuffmptLMJx0q57AAAgAElEQVR9SNK3gDTtiLwaMwa8vOC77+DcOaujEe5Akr4FJOmLvKpRA/r3h6QkmDrV6miEO5CkX8TOnzcVFEuUgPbtrY5GuIJnnzXLL76A5GRrYxGuT5J+EbONwu3cGXx9rY1FuIbu3aF+fYiKgqVLrY5GuDpJ+kVMmnZEfnl5wTPPmPXJk62NRbg+SfpFSGtYvdqsS9IX+TF6tGkSXL3azLYmREHlmvSVUn5KqeeVUieUUqPvsJ+3UmqyUmq9UmqTUqp52vY2SqkNSqnNSqkJdozd5Rw7BidPQrlyZk5UIfKqbFl4+GGzLt03RWHk5Uo/CLgB5DYYfBDgpbUOBf4KfJC2fQowUmvdEQhWSnUoaLCuzta007WrGZglRH6MHWuW06fDtWuWhiJcWK5JX2t9Ums9FUjKZdcOwFKlVH/gdaChUqps2vvilFLTgFJA61vfqJQao5QKV0qFX7x4Md9fwlVIe74ojJYtTQeAa9dg5kyroxGuyt5t+m8AwUB/wNa5rCowG/iYHH4taK2naK1DtNYhFStWtHNIziE1VZK+KDzb1f6kSVKPRxRMgZO+UmqQUmphpk3bgZ1a67eAEOCg1joGiAOeAPYAfYAthYjXZe3ZA5cvm8E29etbHY1wVQMHQtWq5mau7SJCiPzIy43c6kqpcGAMMF4pZfthWRlonGnXb4DSSqn1wDvAy2nbnwEWARuBrVrrbfYK3pVkvspXytpYhOvy8cmovvnJJ9bGIlyT0k72GzEkJESHh4dbHYbd9e4NK1fCrFkwcqTV0QhXdv68+cWYnAxHj0Lt2lZHJJyBUmq71jokt/2kn34RSEw0lTUBevSwNhbh+oKCYOhQ06Y/aZLV0QhXI0m/CPz6K8THQ7Nmpj66EIX14otmOW0axMVZG4twLZL0i4BtFK5c5Qt7CQmBDh3M/LkzZlgdjXAlkvSLgCR94Qi2q/2PPzZdgoXIC0n6DhYba6ZGLFZMpkYU9jVwIFSvDocPw08/WR2NcBWS9B1s7VpzFdauHQQEWB2NcCc+PvDcc2b944+tjUW4Dkn6DiZNO8KRnnzSVN9cuRIOHrQ6GuEKJOk7mCR94Ujly8Ojj5r1iROtjUW4Bkn6DvTHHxARYZp12rSxOhrhrl56ySxnzgQ3rlco7ESSvgPZSi+EhZn2VyEcoVEj6NsXEhLg88+tjkY4O0n6DrRqlVlK045wtHHjzHLSJJP8hciJJH0HSU2V9nxRdLp2NfX2L1yAb76xOhrhzCTpO8jeveZ/wGrVoHHj3PcXojCUyrja//BDqbUvciZJ30F+/tkse/aUUsqiaAwbBlWqwL59GX9/QtxKkr6D2Nrze/WyNg7hOYoXhxdeMOv//a+1sQjnJUnfAW7cyCilLFMjiqL09NNQqpTpObZjh9XRCGckSd8BNm0yNfTvvhsqVbI6GuFJAgPNKF2ACROsjUU4J0n6DiBNO8JKL71kCvwtWAAnT1odjXA2kvQdIPNNXCGKWs2a5qZuSgp89JHV0QhnI0nfzs6fh927TRGsjh2tjkZ4qj//2SynToXoaGtjEc6lmNUBuIq4m3Gcij3F2WtnOX/9PBeuX+By/GWuJFzhSuIVriVeIz4pnpMbOwH/xKf2FtrPeA6tNd5e3hTzKoaPlw8lfErg7+OPv48/pYuXpoxfGQL9AqngX4EK/hWo6F+RKgFVqBpQFX8ff6u/tnBRLVvCvfeaOvuTJsE//2l1RMJZSNLPJCE5gYMXD7Lvwj4iLkcQGR1J5OVITlw5QUxCTN4+5PcRAFyt/i27zu0qVDxlfMtQo0wN7ipzFzXL1KRO2TrUK1ePumXrUq9cPUr4lCjU5wv39te/mqT/8cfwyitQsqTVEQlnoLSTDd0LCQnR4eHhDj/OzZSbbD+znW1ntrHtzDbCz4Rz+PJhUnX28875evtSs0xNqgZUJahUEEElgyhfojyBfoEE+gUS4BtAiWL+PNKpK5cv+DJ31T4aNr2JQpGiU0hOTSYpJYkbyTe4kXSD60nXiU2IJTYxlpgbMVy+cZmL8Re5cP0C5+LOcebaGW6m3MwxfoWiVmAtGlVoROMKjWke1JxmlZrRpGIT+YUgADMqt0MH+PVXU3bZNr2icE9Kqe1a65Bc9/OUpJ+YnMjWqK38cuwXNpzawO+nfychOWtlKm/lTf3y9WleqTmNKjSifrn61C9fnzpl61DRvyIql6G1e/aYn9VVq0JUVOFG4mqtuXzjMn/E/sHJ2JOcuHKCYzHHOBpzlCPRRzgWc4zk1OTb3uelvGhYviHBlYO5p8o9hFQN4Z4q91Dat3TBgxEu68cfYcAAM63i0aNmAJdwT3lN+m7dvHPyykmWHF7CsshlbDi5gfik+CyvN6nYhHbV2tG6WmtCqobQrFIz/Ir5Ffh4K1ea5b33Fr70glIqvZ3/7ip33/Z6UkoSR2OOcvDiQQ5cPMDeC3vZe2EvEZciOHjpIAcvHeSbfabylkLRqEIj2lVvl/5oWrEp3l7ehQtSOL3774cmTeDAAZgzBx57zOqIhNXc7kr/4MWDLNi/gO8OfsfeC3uzvNa8UnN61OlBWK0wOtboSHn/8oUNN4vu3WHNGpg3D4YOtetH59mNpBvsv7ifnWd3suPsDsLPhrP73G6SUpOy7FfatzTtq7enU81OdLmrC22qtSnUCU84r1mzzOxaDRvC/v3gLed6t+RxzTufbvuUz8I/Y9+FfenbAooHcG+9e+nXoB+96vaicqnK9gw1i7g4KFfO9I2+cMFMY+csEpMT2X1+N79G/cqvUb+yNWorJ66cyLKPr7cv7aq3o2utrnSr3Y221dtS3FvaAtxBUhLUr28Gai1YAIMHWx2RcASPS/ovr3yZib9NJNAvkIGNBjK4yWC61e6GbzFfB0R5u6VLoV8/aNvW3DhzdqevnmbzH5vZcHIDG05uuO1Xkb+PP51rdqZnnZ70qNODFkEtcr2nIZzXZ5/Bs8+ae047d0rlV3fkcUk/4lIEx2KO0b1Od0uuUMeOhcmTTX/of/2ryA9faJfjL7Ph5AbWnljLmuNr2H9xf5bXK5eqTK+6vbi37r3cW/deuzeNCcdKSIA6deDsWfjhB+jf3+qIhL15XNK3Wv36cOQIbNkC7dtbHU3hnYs7xy/HfmH18dX8fPRnzlw7k/6al/KibbW29Knfh771+xJcOVh+BbiAiRPh5ZehdWv47Te52nc3kvSL0NGjUK+eqXB48aIpduVOtNbsv7iflUdWsvLISjac3JDlxnDVgKrcX/9++jXsR/fa3WXQmJOKj4datczf6MqVppeZcB92S/pKKW/gY6AZ4A08o7Xem81+g4CxaU+LAUFa6/pKqTeBYcA5IFZrPeBOx3PFpP/pp/DcczBoECxcaHU0jnct8Rprjq9hWeQylkUuy/IroESxEvSq24sBDQfQr2E/KvhXsDBScat//9uM1O3YETZulKt9d2LPpD8UCNNaP6OU6gT8U2t9x6LBSqkngSpa67fSkv4JrfX0vATuikl/wAAzCGbqVHj8caujKVpaa3ad28WSw0v4MeJHtp/dnv6al/Kic83ODGw0kIGNB1KzTE0LIxUA166Zq/3oaDPRSrduVkck7MWeSf9/wM+kXeUDTbTWd91hfz/gN6Cz1vqqUuolYCRwA1iotf44m/eMAcYA1KxZs9VJFyoCnphoumdevw6nTkGNGlZHZK2oq1EsiVjC4ojFrDm+Jsuo4dZVW/Ng4wd5qPFD1C9f38IoPds778A//gGdO8P69XK17y7snfTbACuA94BDWuu6d9j/FaC41vq9W7b7ARuAR7TWETm939Wu9FevNnXzmzc3ZRhEhisJV1geuZxFhxaxPHJ5lhHRLYJaMKjxIIY0HULDCg0tjNLzXL1qrvZjYszfr0zp6R7ymvTzUk9/O7BTa/0WEAIcTDvAIKVUlhZspVRp4Angk2w+JyVteS0Px3QZy5ebZZ8+1sbhjAL9AhnRfAQLBy/k0quXWDR0ESNbjKS0b2n2nN/DP9f9k0aTG9Hisxa8s+EdIi9HWh2yRyhdOqPe/vjxpjCb8Bx5udL3Ab4GagDJwNNa60il1Ni09WaZ9v0XEKe1/m+mbX8DegEa+FxrveBOx3O1K/1GjSAiwvxM7tLF6mhcQ2JyIquPrWbhgYUsPrSY2MTY9Nfurnw3Q5sOZWizodQKrGVdkG7u2jWoXRsuXzbll2VqT9cnXTaLwLFjULculCljusH5+FgdketJTE5k1bFVLNi/gMWHFnPtZsYPwfbV2zOs2TCGNB3i0BIansrWk6ddOzO+RNr2XZsk/SIwebIZiTt4sKlpIgonITmBn478xPz98/kh4of0ewBeyotutbsxvNlwHmz8IIF+gRZH6h7i4szV/qVLppmyd2+rIxKFYc82fZEDac+3L79ifgxoNIC5D83lwp8v8M1D3zCg4QCKeRVj9bHVPP7j41SeUJmHFjzEdwe+u20+BJE/pUrBX/5i1l9/HVKznz9IuBm50i+gGzdMVc2EBFPPpLK0PjhMzI0Yvjv4Hd/s+4a1x9eiMX+zZXzL8FDjh3i4xcOE1QrDS8k1TH7duGFGk585YwYWDhpkdUSioKR5x8FWrDBX+K1agQuE6zbOXDvD/H3zmb13NjvO7kjfXr10dUY0G8HIFiNpHtTcwghdz+efwzPPmE4Je/e6XxkRTyHNOw4mTTvWqBpQlZfbv8z2Mds5+NxB3uj8BrUCaxF1NYr/bPkPLT5vQfDnwXyw5QPOXjtrdbgu4U9/MhU4Dx2C2bOtjkY4mlzpF4DW5ifxsWPuU1XTlWmt2fLHFmbvmc38/fOJSYgBzA3gHnV68EiLRxjYaCAli5e0OFLnNXs2PPII1KwJhw+Db9FMQyHsSJp3HOjAAWjaFCpUgHPnZPo5Z5KYnMjyyOXM2jOLpYeXplcDLelTkoeaPMSolqOk/T8bKSlmgpX9+00J5hdftDoikV/SvONAS5aYZZ8+kvCdjW8xXwY2Hsj3Q7/n3J/P8Vnfz2hfvT3Xk64zc/dMus/sTq2Jtfj7L38n4lKO1UA8jrc3/N//mfV33jGlGoR7kiv9AujUCTZvlt4OruRI9BFm7Z7FzD0zs8wP3KZaG0a1HMXQpkM9fjYwrc2o8k2bTBfOd96xOiKRH9K84yCXLkFQkLkyunTJ1DERriNVp7Lp1CZm7p7Jgv0L0kcA+3j50K9hP0a1HEXver3x8fbM4dVbt0KHDlCiBERGQrVqVkck8kqadxxk+XIziCUsTBK+K/JSXnS5qwtT+0/l3J/PMefBOdxb915SdArfH/yeAfMGUO3Dary88mV2ndtldbhFrn17ePBB03//zTetjkY4glzp59PgwfDtt/Dxx/D881ZHI+zl9NXTzNk7hxm7Z3Dg4oH07S2CWjCq5Sgebv4wQaWCLIyw6EREmI4KWpt++02aWB2RyAtp3nGAmzdNj51r1+D4cVOTXLgXrTXbz25n+q7pfLPvG6JvRAPgrbzpXb83o1qOol+DfvgWc+8+jc8+C599Bn37wtKlVkcj8kKSvgOsWmVK0DZrZq6AhHtLTE5kWeQyZuyewfLI5emzgJX1K8vwZsMZFTyK1lVbo9ywPOX581C/vrnAkdLLrkHa9B3A1lWzXz9r4xBFw7eYLw82fpAfhv3A6XGn+ejej2gZ1JKYhBg+Df+UtlPb0vTTpvx70785ffW01eHaVVCQ6cEDMG4cJCffeX/hOuRKP4+0NkPVT5yQUbiebve53czYPYM5e+dw4foFwNwg7lmnJ6ODRzOg4QBK+JSwOMrCS0iAxo3N3/xnn8HTT1sdkbgTad6xs927ITgYKlUyFQllUJZISkli5ZGVzNg9gyWHl3Az5SZgqn8OaTqEUS1H0aFGB5du/lm4EIYMgYoVTRfOMmWsjkjkRJp37GzxYrMcMEASvjB8vE3f/m+HfMuZcWeY3Gcyrau2JjYxli93fEmnrzvRYFID3l7/NievnLQ63AIZNAg6djQzw8lgLfcgV/p5FBxsrvZlhiGRmwMXDzBj1wxm753NmWtn0reH1QpjVMtRDGoyiFLFS1kYYf6Eh0ObNqbk8p49pgSzcD7SvGNHx4+b9vyAAHPFIxUIRV6kpKaw+thqZuyewaJDi9Jn+vL38eehxhnF37y9nP+n4xNPwLRpphfPypUyn64zkqRvRx9+CK+8AkOHwrx5VkcjXFFsQiwLDyxkxu4ZbDq1KX179dLVGdl8JI+2fJTGFRtbGOGdXbwIDRrAlSuwaBE88IDVEYlbSdK3o86dTRGqefNM4heiMI5GH2XWnlnM3D2T41eOp28PqRrCoy0eZVizYVQsWdHCCLP3ySfwwgtmUOKBA6Y+j3AekvTt5Px5qFIFfHzM1Y7U2xH2orXOKP52YAFXE00942JexehTvw+PtniU+xvc7zSjf5OT4Z57zMDEN9+E8eOtjkhkJknfTr78EsaMMbXzly2zOhrhrm4k3eDHiB+ZuWcmPx35iRSdApjRv0OaDuGRFo84RffPDRsgNNTc19q3z8wgJ5yDdNm0k0WLzHLgQGvjEO6thE8JhjYbyrIRy4gaF8WHvT4kuHIwMQkxfLH9Czp93Yl6n9Rj/NrxRF6OtCzOLl3g0UchMRGee84MWhSuRa707+DqVTMoJSkJzp41Q9OFKEp7z+9l9p7ZzNk7h9PXMko9tK3WlpEtRjK06dAib/+/cMF024yJkftczkSad+zANll0ly6wfr3V0QhPlpKawtoTa5m9ZzbfHfyOuJtxgGn/v6/efTzc/GH6N+yPv49/kcRja/asXBkOHZKRus5AmnfsYMECsxwyxNo4hPD28qZHnR5Mf2A65/98nrkPzqVP/T5orVl6eCnDvxtO0IQgRi0exc9Hf06vCOoojz9u6k+dO5dRmE24BrnSz0FsrKmzk5Rkau1Urmx1RELc7sL1C8zbN485e+fw++nf07cHlQxiWLNhPNz8YUKqhjjkBvCePdCqFaSkmC7NHTrY/RAiH6R5p5BmzTI3rEJDYd06q6MRIneRlyOZu3cuc/bOITI642Zv/XL1GdF8BMObDadhhYZ2Pebrr8P//Z9p49+5E/z87PrxIh8k6RdS//6mfv7kyWYWISFchdaa8DPhzNk7h3n75nH++vn01+6pcg8jmo1gaLOhVC9dvdDHSkgwdakiIuCNN+Dttwv9kaKA7Jb0lVLewMdAM8AbeEZrne28UUqpBODXtKf/01ovUkq1ASakvXer1vrPdzqeMyR9W9NOcjKcPi1NO8J1Jacms+7EOubsncP3B79PHwCmUHS+qzPDmw1nUJNBVPCvUOBjbNxoOjsUKwbbt0OLFvaKXuSHPZP+UCBMa/2MUqoT8E+tdbaTpymlTmita92ybRfQX2t9Sim1Ou39W3I6njMkfVvTTlgYrF1raShC2E1CcgLLI5fzzb5vWBKxhMSURMD0AOpZpyfDmg1jQMMBlPHLf1cc25y6rVrBr7+aE4AoWvbsvdMBWKqU6g+8DtypUTBZKbVBKfW9UqqOUqoskATEKaWmAaWA1tkEO0YpFa6UCr948WIeQnIs6bUj3JFfMT8ebPwgCwcv5MKrF5jxwAzuq3cfWmtWHFnBqMWjCJoQxMD5A5m/bz7Xb17P82e//z7UqGGu9N9/34FfQhRaXq70/we0AVYA7wGHtNZ1c3nPg8Bg4FlgH7Ab+BvQBfDSWv8vp/dafaV/5Ypp2klJMb12ZECWcHcXr1/k+4PfM2//PNafWI/G5AR/H3/ub3A/Q5oMoU/9PrlOAbl6NfTsaepUbdsGLVsWRfTCxp5X+tuBnVrrt4AQ4GDaAQYppRbmdHwgRmsdA8QBTwB7gD5Ajk07zuC770w3zbAwSfjCM1QsWZGnQp5i7ai1RI2LYuK9E2lfvT3xSfEs2L+AQQsHUWlCJUZ8N4LFhxanzwtwqx494JlnzP8/jz4KN28W8RcReZKXK30f4GugBpAMPK21jlRKjU1bb5a2XyXgOyARuAA8p7WOUUp1w/xCSAJ+Tjt55MjqK/1u3Uw7/rRp8Kc/WRaGEJY7eeUkCw8sZMH+BWw7sy19e0DxAPo17MfgJoO5r959+BXL6KcZF2eu8I8dk948RU26bBZAVBTUrAnFi5uSyjK0XAjjWMwxFu5fyIIDC9hxdkf69lLFS9GvQcYJoIRPCTZuNONblDI9e2TQVtGQpF8A//0vvPaamQx6YU4NV0J4uCPRR/j2wLcsPLAwywmgpE9J+jboy0ONH2Lr1w8w8YPi1K4Nu3bJPBRFQZJ+AdgmP5fp4ITIm2Mxx/j2wLd8e+DbLE1AvgTgN30nsSfqMnzkTebOKm5hlJ5Bkn4+7d8PzZpBYKApIiWTnwuRPyeunOD7g9/z3cHv2PLHFrjYCL7YDsn+tBz7fzw7ugIDGg4gqJT0kHAESfr59Pe/w3vvwZNPwpQpRX54IdzK6aunWXxoMR9PvsnhmS+D7xV4OhhV9hQda3ZkYKOBDGw0kNpla1sdqtuQpJ8PqalQpw6cPGnq5nfpUqSHF8JtaQ19+yeyYqkvgXUjuD6yFUkqY9BXy6CWPNDoAR5o9AAtg1paPh2kK5Oknw+2eT9r1IATJ8BLZhkQwm6io+Huu+HUKRj7YiKdnljMokOLWBa5LH0yGIC7ytzFgIYDGNBoAJ1rdsbH28fCqF2PJP18GD0aZswwZWLfeadIDy2ER9i61fyCTk6GH3+Efv0gMTmRNcfXsPjQYn6I+CFLNdCyfmXpU78P/Rv2575691HaV7r/5EaSfh5dvQpVqkB8PERGQr16RXZoITyKrUt02bKmRk/tTM35qTqV36J+44eIH/gh4gcOXTqU/pqPlw9htcLo16Af/Rr2o1ZgraIP3gVI0s+jqVPNzVuZLEUIx0pNhQEDYOlS09yzeTOUyKGcT8SlCJYcXsKSw0vYdGoTqTo1/bVmlZrRr0E/7m9wP22rtcXby7uIvoFzk6SfRx06mJ+eM2aYeiFCCMeJiYGQEFOmYfRo+OorM3L3Ti7HX2Z55HKWHF7CyiMruXbzWvprFfwr0Lteb/rW78u99e4l0C/QsV/AiUnSz4ODB6FJEwgIgLNnoWTJIjmsEB5t924zqfqNG/D55/DUU3l/782Um2w4uYElEeZXwPErx9Nf81bedKjRgb71+9K3QV+aVmzqUb2BJOnnwWuvmXZG6ZsvRNGaPRseecSUYV63rmD1ebTWRFyOYOnhpSyLXMamU5tITk1Of7166er0qdeH3vV70712dwJ8A+z3BZyQJP1cJCWZLprnz8OWLebKQwhRdF58ET7+2MxfsW2bKXZYGLEJsfx89GeWRS5j5ZGVWXoD+Xj50KlmJ3rX68199e6jWaVmbvcrQJJ+LhYvhoEDoVEjOHAg93ZFIYR9JSdD795m8pWWLc2NXXs1sabqVHae3cnyyOWsPLqSX6N+zXIzuGpAVe6tey/31r2XHnV6UN6/vH0ObCFJ+rno1QtWrYIPPoBx4xx+OCFENqKjoW1bOHIEHnrITFXqiMGR0TeiWXV0FSuPrmTlkZWcizuX/ppC0bpaa3rV6UWvur1oV72dSw4Mk6R/B4cPQ8OGprvY6dOm37AQwhqHDkG7dhAbC3/5i+Pn2NVas+f8Hn46+hMrj6xk06lNJKUmpb8eUDyAsFph9Krbi551etKgfAOXaAqSpH8H48bBRx/B44+bfvpCCGutWgV9+pgmn/z26CmsuJtxrD+xnlXHVvHT0Z+yDAwDqFG6Bj3q9KBHnR50r93daauEStLPQXw8VKtmJkDfvh3uucdhhxJC5MNXX5kLMS8vWLLEnASs8EfsH6w6toqfj/7ML8d/4VL8pSyvN6vUjO61u9O9dndCa4U6TYkISfo5sP1htW0Lv/7qsMMIIQrgH/8w9a9KljRdOUNyTWGOlapT2XN+D6uOruKX47+w4eQGbiTfSH/dW3kTUjWEbrW70a12NzrU6IC/j78lsUrSz4bW5o9oxw4ZgSuEM9IaRo2CWbOgQgXYtMncf3MWicmJbI3ayi/HfmHNiTX8fvr3LGMDinsXp221tnSt1ZWwWmG0r9E+y8TxjiRJPxu//WZuGJUrZ27g+hXNv4UQIh+SkkyNnhUrTN/9zZuhenWro8retcRrbDy1kbXH17LmxBp2nt2JJiOn+nr70q56O8JqhRF6VyjtqrejhE8OBYcKSZJ+NoYONV3CXnsN/v1vhxxCCGEH169Dz56mLlbjxmbOiwoVrI4qd9E3otl4ciNrT6xl7Ym17Dm/J8vrxb2L06ZaG0LvCqXLXV1oX7293UYKS9K/xfHjpmyyl5eZKKVaNbsfQghhR9HRpgb//v2mKucvv7he9+rL8ZfTfwmsP7mePef3ZPkl4K28ubvK3XSp2YXOd3WmU81OVPAv2NlNkv4tbEO+H33UtOcLIZzf2bMm8R85Am3amK6dpZ2js0yBxNyIYeOpjWw8uZENpzaw/cx2UnRK+ut3lbmLEy+dKNBnS9LPJCbG1Nm5ft1U+GvRwq4fL4RwoD/+MPNdHD9uCrP99BOUKmV1VPYRdzOOrX9sNSeCUxupX64+U/oVrPpjXpN+sQJ9uov54guT8Hv1koQvhKupUQPWrDFX/Fu2wH33wfLlrn3Fb1OqeCl61u1Jz7o9i+yYbj8FeGKiadYBeOUVa2MRQhRMrVom8deoYXrz9OxpfsGL/HP7pD9njmkXbN7c/KEIIVxTvXqmF0/t2vD779C9O1y6lPv7RFZunfSTkuDdd836X/4i5ZOFcHW1asH69VC/PuzcCZ07mzZ/kXdunfTnzDFzcTZoAMOGWR2NEMIeatQwib95c1Ohs2NHsxR547ZJPznZ1PAAeOMN8Pa2Nh4hhP1UqWISf4cO5kq/Uycz4l7kLtekr5TyVkpNVkqtV0ptUko1z2E/f6XUbKXUWqXUb0qphmnb31RKHVJKrVNK/WDvL5CT2bPh6FHzM3D48ENL67kAAAyISURBVKI6qhCiqJQtm1GS+fJlCAuDRYusjsr55eVKfxDgpbUOBf4KfJDdTlrreGC81rorMA14NtPL72utw7TWAwobcI6OHIHwcLh+/bar/GIe0TFVCM/j72+mPn38cUhIMLNvffSRKdwmspeXpN8BWKqU6g+8DuRY805rfTRttSpwLG39CjBWKbVRKfVCdu9TSo1RSoUrpcIvXryY9+gz++wzaN0aAgKYXeVVjh6FemUvMSJ5ppl1+dq1gn2uEMKp+fjAl1+aThtam0mSnnvOdOQQt8t1RK5S6n9AG2AF8B5wSGtd9w77PwA8BjyktU7OtN0P2AA8orWOyOn9BR6R+957MGcONw6dpEHKAaKowUwe4RFmZ+xTvbqp3tSoUcajYUOoWlW69gjhBr75Bh57zIzP6dIFvv0WKla0OqqiYbcyDEqpR4F2WutnlVLtgde11vcrpQYBQ7XWgzPt+zjQDXhMa33zls/xATYDD2itz+R0vMKWYXjvnRT+/g9vgmvFsP3Rj/E6dAAOHDAT4968mf2bSpUyXXwaNjTLBg3MzYD69SEwsMCxCCGK3m+/wcCBZnzOXXeZ5p/gYKujcjx7Jn0f4GugBpAMPK21jlRKjU1bb5a2XwjwGyaxpwI3tda9lFJ/A3oBGvhca73gTscrTNK/cMEM4Lh2DVavNoM30iUnm+IdBw9CRITp43XwoDkZXL6c84dWqJBxAqhXzyzr1jXrrlbyTwgPceaMSfy//27mzfj0U/MLwJ15ZMG1554z/7h9+sCyZfl44+XL5kRw+LB5RERAZKS5OXzjRs7vK1sW6tQxJ4E6dbI+atSQO8hCWCghAcaOhWnTzPPHH4dPPoESjpnDxHIel/QjIqBpU3MjZ88es15oqanmkuHIEXMSiIw0/UCPHjXbrl/P+b3e3ibx165tHrVqZSxr1TIdjWXwgBAO9/XX8Oyz5iTQvDnMmwdNmlgdlf15XNJ/4AH44Qd48kmYUrDKpPmjtWlPsp0Ejh0zzUfHjpnHmTN37jfm42NuLN91V8ajZs2MZY0a7ntJIkQR270bBg82121+fqZb51NPuVf/DY9L+r/9BuPHm7N6lSoOCCy/EhPh5ElzIjh+3EzXdfy42XbiBJw/n/tnVKiQcQKwPapXz1hWqwbFizv6mwjhFuLi4IUXTI4A6N/fXCAGBVkbl714XNJ3OTduwKlT5iRw8qRZtz0/dcqMLU9Ozv1zgoIyTgA5PUqXdq9LGiEKYd48c5V/9SqUL2+G+AwenPv7nJ0kfVeXkmJ+DfzxR8YjKirr+pkz5r5Dbvz9zVgE26NKlYxl5keZMnJyEB7h1ClzY3f1avN8yBAz74YrX/VL0vcEyclw7hycPm0eUVEZ66dPm5PC6dN3vuGcWYkSULmyeVSpYpZBQbcvg4LkfoNweVrD55/Dq6+a/0XKloUJE0zXTle89pGkLwytzcCF06fNaJUzZ8zDtn72rDlxnD1rGj3zKiDAnAQqVco4EQQFmee3PgIDXfP/IuERjh+HZ54xc++CKdw2aZKdegAWIUn6Iv/i4swJwHYSsK2fO2eammzL8+fzV9jEx8fclK5UyYyJtz0qVMj+ebly0p1VFCmtYe5ceOklMxtXsWLmpu/48a4zF68kfeE4WpsJSs+fN91WbSeCCxcynl+8mLGe32J3Spnf2hUqZH2UL28emdfLlctY9/FxzPcVHuPyZVOZ94svzJ955crw9tumycfZr0Mk6QvnkZBgTgK2x4ULZnnpUvbL6OiCHScgIOvJIPMj87ayZTOWZcuajttCZLJjhxnh/+uv5nnz5qa9v2dP522plKQvXFdysvklYTsJXL5sHpcuZV1mfkRH560nU3b8/LKeBDI/AgNvf27bFhgIJUs6bxYQhaI1zJ8Pf/2r6UkN0LWrKeHcvr21sWVHkr7wLKmpEBtrTgAxMRkng5gYc0LIvB4dbdZtzwtTeN3bO+NEEBhour3eurx1/daHDLBzagkJ8L//wfvvw5UrZtv995v2/pBcU2zRkaQvRF5oDfHxWU8E2T2uXMl4ZH4eH1/4GHx9M04ApUtnXc/LIyDALH19Cx+LyNGVK6aJ56OPMv7Z+/SBf/wD2rWzNjaQpC9E0bh50/zCsJ0MYmMznue2bnukpNgnluLFM04AAQG3r9/6KFUq5/VSpaRKbA7OnzfJ/9NPM5J/ly7w2mvQuzd45WU+QgeQpC+EK7D90oiNNXUBrl4169euZZwUbl237Wdbt23PS9mO/PDzyzgBZH5kPjGUKmXua9xpvWTJjPUSJazLinZ26ZK56p80yfwzgKne+cILMHKk+cpFSZK+EJ5Ea1Pkz3YiuHbt9vVbH3FxOa/HxRX8xnhu/P0zTgS3nhhufS3zc3//jOfZLf39zYmqiE8qV6+aOXonTjSD4sHcwnn8cXj6aTPfUlGQpC+EKDitTVFA2wkg88ng2jVTtyDz+vXrWdfj4rJft8c9kNyUKHH7ySDzw/Z65vWctmV+3PraLeNCbt40c/J+8klGV08wM/iNGQMDBjj2toskfSGE80lNNYnfdhLI/IiLy/paXtZv3Mi6npBQdN/F2/v2E0PaY1tSMJPPPciCs525kWIyfVnf64xosptRrfYRUif6/9u7mxCr6jCO499fDSI2vYFDIUGFlFQIatMEZgQtZiE5iC8LMUIspSJpGxQI1aJF0RtuJlsIykSBtcgCF5Na2tsdSjeWYWhLFWqh43tPi3PHmWxm+t/rnDP33PP7wDB37vzPzPPMy+8czr3nuWjWmG1mzszeurqaflTYoW9m1XP5chb+Z8+O7hyuvj2yoxi5f3h49PbY9xPdN/JxwgPwf3EzO1jLB2zgIKOvzn4vv7KGAdYwwDyOjG7Q05O9OEgTHPpmZnm6ePHfO4Lx3s6du3L74NFOth24hx0/38+JM51Xvsz8W/5g5ZxvWTl7Hw8snIHeebupchz6ZmYt6NIlGByEgQHYuXP0mT8AixZBrdbcRd6pod8ez50yMyuJjg7o7c1etvHECdi1C9avz8ZDzZ2b/1QPH+mbmbWAkZFTXV3Nbe8jfTOzEunoaD7wG+HQNzOrEIe+mVmFOPTNzCrEoW9mViEOfTOzCnHom5lViEPfzKxC/jf0JV0vaYukvZK+kTS/kXWSeiTtk7Rf0ptT3YCZmaVLOdJfBVwXEY8BLwFvNbiuH3gyIh4BFkhafI01m5lZk1JCfzHwuaQ+4GVgXuo6SbcCF4HTkj4EOoGHrt5Q0kZJNUm1kydPNtOHmZklSD2n/wqwAOgDJnshzvHWzQG2A+8BO8bbKCL6I6I7Irq7irgO2cysolJCfwj4KSJeBbqBwwCSVkn6ZLJ1EfEncBp4BjgELAUOTGH9ZmbWgI6ENQNAr6S9ZEfvz9bvvx24L2Hdc8CnZKd5dkfEj5N9s6GhoVOSjk/w6dnAqYSa25F7r56q9g3uvZne70xZ1HKjlScjqZYyOrQduffq9V7VvsG959m7n6dvZlYhDn0zswopW+j3T3cB08i9V09V+wb3nptSndM3M7NrU7YjfTMzuwYOfTOzCmmp0E8d7lZf2yPpS0mDkp4uss48NDDYbqakj+trapJWFF3rVKv3tEnSMUnrJlmX/PdRFg30PkvSdklfSfpe0kTjUEohte8x61+QdEnSXbkXl7NGes8j51IuzirSlaFtkpaQDW3rvXqRpBuBd4G+iGiXYT1JvQMPA+cjYomkB4HNwM4C68zDbcBZJhjTMUbqz6hMknqPiGFJmyPiqKSNwPPAi0UUmJPU3zmS7gaW0T5X8yf1nlfOtdSRPunD3R4FZgDbJH1dX192qb1/B3RK2gq8AbxeUH25iYjjEbGV7KrtyaT+jEqjgd6JiKP1m3OA33MtLGepfUsS8D6wCfi7iNry1sDvPJeca7XQh7ThbjcBtYhYCqwg2xu2g9TebwB+IPuj+c/U0jaXOvyvLUlaDiwEtkx3LQXZCAxGxJHpLmQa5JJzrRb6qcPdfmN0zsQF4EyhVeYjtfc+4FBE9JP9Q2wovNKCpAz1m57K8jdO79TP6a4GVkdEW+7wxul7GbBc0h6ynf1HZX88YyJF5VyrndNPGu4WEUOSfpF0gOxot8znNkekDrb7Alhb/yfoAF4rssg8SLoD+IzstMV5SY9HxFOkD/UrrdTeJXWTXbSzH9gt6UJElPbxjNS+I+KJMdvsAdZFxLFiq51aDfSeS8754iwzswpptdM7ZmaWI4e+mVmFOPTNzCrEoW9mViEOfTOzCnHom5lViEPfzKxCHPpmZhXyDykXkMgkXJsvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xs_nd, f_ys_nd_1, color='r', lw=2, label='df1 = 1, df2 = 1')\n",
    "plt.plot(xs_nd, f_ys_nd_2, color='g', lw=2, label='df1 = 15, df2 = 12')\n",
    "plt.plot(xs_nd, f_ys_nd_3, color='b', lw=2, label='df1 = 100, df2 = 100')\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
